{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:L73RTWVZTKB4SF3RGO6F2KI4V5","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3ece457e82a092b5894b49bc5f9ee9128fa7eb7ea47e8193d6fe4096acb1eccc","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-05-25T11:30:09Z","title_canon_sha256":"8008412a9b6b49d84b322015d279ce11c4e0dd5f377fc6abf5c3480c83d8f608"},"schema_version":"1.0","source":{"id":"2605.25723","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.25723","created_at":"2026-05-26T02:04:52Z"},{"alias_kind":"arxiv_version","alias_value":"2605.25723v1","created_at":"2026-05-26T02:04:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.25723","created_at":"2026-05-26T02:04:52Z"},{"alias_kind":"pith_short_12","alias_value":"L73RTWVZTKB4","created_at":"2026-05-26T02:04:52Z"},{"alias_kind":"pith_short_16","alias_value":"L73RTWVZTKB4SF3R","created_at":"2026-05-26T02:04:52Z"},{"alias_kind":"pith_short_8","alias_value":"L73RTWVZ","created_at":"2026-05-26T02:04:52Z"}],"graph_snapshots":[{"event_id":"sha256:1eace9cdb60a1750859876fd7659b07fa82d85c7d2b1ae92cae139f5e31114f9","target":"graph","created_at":"2026-05-26T02:04:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.25723/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The stability and deformation theory of Einstein metrics traditionally relies on the classical Berger-Ebin transverse-traceless gauge, which structurally decouples the scalar trace from the divergence-free component of metric perturbations. In the present paper, we introduce a new spectral-geometric framework based on the Chen-Nagano gauge condition. This condition naturally arises from the harmonicity of the identity map and is intrinsically satisfied by the Ricci tensor itself via the contracted second Bianchi identity. Unlike the classical transverse-traceless framework, the Chen-Nagano gau","authors_text":"Sergey Stepanov","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-05-25T11:30:09Z","title":"Spectral Properties of the Chen-Nagano Gauge on Einstein Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.25723","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:337a01552ff1edf9c70e479c40c4fc0fc0732c14829185322ca21c5ca1a25835","target":"record","created_at":"2026-05-26T02:04:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"3ece457e82a092b5894b49bc5f9ee9128fa7eb7ea47e8193d6fe4096acb1eccc","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-05-25T11:30:09Z","title_canon_sha256":"8008412a9b6b49d84b322015d279ce11c4e0dd5f377fc6abf5c3480c83d8f608"},"schema_version":"1.0","source":{"id":"2605.25723","kind":"arxiv","version":1}},"canonical_sha256":"5ff719dab99a83c9177133bc5d291caf646ac56b1a0b5fd4632dc5c0e4681324","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ff719dab99a83c9177133bc5d291caf646ac56b1a0b5fd4632dc5c0e4681324","first_computed_at":"2026-05-26T02:04:52.138375Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T02:04:52.138375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W8C6jSrnY9p87qMw542WL/xjZZy0h60TyTT79lgA9zt1VQS0B1XgQi8I9I8rOMI3iuAJW0KWF85RnmxZumnJAw==","signature_status":"signed_v1","signed_at":"2026-05-26T02:04:52.139184Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.25723","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:337a01552ff1edf9c70e479c40c4fc0fc0732c14829185322ca21c5ca1a25835","sha256:1eace9cdb60a1750859876fd7659b07fa82d85c7d2b1ae92cae139f5e31114f9"],"state_sha256":"5a08f3d2cde6cc4da161d9aaf9a0ba3e8e84653de6a7359c9c6cc2dba94a25f3"}